A family of semianalytical solutions is presented describing multipolar vortical structures with zero total circulation in a variety of two-dimensional models. Analytics are used to determine the form of a multipole edge, or separatrix, and the solution outside this separatrix. The interior is solved using a Newton-Kantorovich (successive linearization) procedure combined with a collocation method. The models considered are the quasigeostrophic f- and γ-planes, with either the rigid-lid or free-surface conditions. A multipole, termed also an (m+1)-pole, is a vortical system that possesses an m-fold symmetry (m≥2) and is comprised of a central core vortex and m satellite vortices surrounding the core. Fluid parcels in the core and the satellites revolve oppositely, and the multipole as a whole rotates steadily. The characteristics of the multipoles are examined as functions of m and a parameter that incorporates the Rossby deformation radius, γ-effect, and the vortex's angular velocity. The analogy between the β-plane modons and γ-plane multipoles is tracked.
|Journal||Physics of Fluids|
|State||Published - Jan 2007|
Bibliographical noteFunding Information:
This research was supported by Binational Israel–U.S. Science Foundation (BSF) Grant No. 2002392. We thank G. J. F. van Heijst and the two anonymous referees for helpful comments on the manuscript.
- Geophysical fluid dynamics